Calculate, estimate, and interpret average rate of change for advanced function types.
Find the average rate of change of a function on an interval
Problem
Find the average rate of change of \(f(x)~=~x^3\) on \([1,~3]\).
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What this problem is really about
Average rate of change is a secant slope, so preserve the same endpoint order in both differences. Evaluate the function at the two interval ends, subtract outputs, and divide by the full change in input rather than by an endpoint itself. The result describes output units gained or lost per input unit across the whole interval.
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